Exponential Functions

On Monday we learned about Exponential Functions.

The function f(x) = ab^x were a and b are real numbers such that a is not equal to zero,

b is greater than zero and b is not equal to one, is an exponential function where :

a is constant

b is a base

x is an exponent

Basic Curve : f(x) = a^x where a > 0

y = a ^-x will reflect the basic curve in the y- axis.

y = -a ^x will reflect the basic curve in the x- axis.

y = a ^x-h+k will shift the basic curve right by ‘h’ and up by ‘k‘

**Read ‘h’ values as opposite, ‘k’ values as is.**

An exponential function is said to be an increasing function when "a" is greater than 1.

An exponential function is said to be a decreasing function when "a" is greater than 0 and less than 1.

Note:

Example #1:

Sketch the following exponential functions on the same Cartesian plane.